Cartan Connections on Lie Groupoids and their Integrability
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Cartan Connections on Lie Groupoids and their Integrability
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| Creator |
Blaom, A.D.
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| Description |
A multiplicatively closed, horizontal n-plane field D on a Lie groupoid G over M generalizes to intransitive geometry the classical notion of a Cartan connection. The infinitesimalization of the connection D is a Cartan connection ∇ on the Lie algebroid of G, a notion already studied elsewhere by the author. It is shown that ∇ may be regarded as infinitesimal parallel translation in the groupoid G along D. From this follows a proof that D defines a pseudoaction generating a pseudogroup of transformations on M precisely when the curvature of ∇ vanishes. A byproduct of this analysis is a detailed description of multiplication in the groupoid J¹G of one-jets of bisections of G.
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| Date |
2019-02-18T15:14:02Z
2019-02-18T15:14:02Z 2016 |
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| Type |
Article
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| Identifier |
Cartan Connections on Lie Groupoids and their Integrability / A.D. Blaom // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53C05; 58H05; 53C07 DOI:10.3842/SIGMA.2016.114 http://dspace.nbuv.gov.ua/handle/123456789/148549 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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